Cremona's table of elliptic curves

28896 = 2⁵ · 3 · 7 · 43

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 43-	Signs for the Atkin-Lehner involutions
Class	28896f	Isogeny class
Conductor	28896	Conductor
∏ cp	32	Product of Tamagawa factors cp
deg	11264	Modular degree for the optimal curve
Δ	2557122624 = 26 · 32 · 74 · 432	Discriminant
Eigenvalues	2+ 3+ -2 7-  0 -2  2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-714,-6696]	[a1,a2,a3,a4,a6]
Generators	[38:140:1]	Generators of the group modulo torsion
j	629863565248/39955041	j-invariant
L	4.0100138149975	L(r)(E,1)/r!
Ω	0.92714565980886	Real period
R	2.1625586942963	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	28896o1 57792bo2 86688bs1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 28896f1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
+	+	-2	-	0	-2	2	4	0	6	4	2	-6	-	-8	6	0	-6	-4	-8	-6	-12	-16	6	2

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Quadratic twists for elliptic curve 28896f1

-4	8	-3
28896o1	57792bo2	86688bs1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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